What is x^2+4y^2+20x-40y=-100 ?

The solution to x^2+4y^2+20x-40y=-100 is Ellipse with (h,k)=(-10,5),a=10,b=5

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x^2+4y^2+20x-40y=-100

x^{2} + 4 y^{2} + 20 x - 40 y = - 100

(h, k) = (- 10, 5), a = 10, b = 5

Solution steps

x^{2} + 4 y^{2} + 20 x - 40 y = - 100

Rewrite

x^{2} + 4 y^{2} + 20 x - 40 y = - 100

in the form of the standard ellipse equation

\frac{( x - ( - 10 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - 5 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 10, 5), a = 10, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 10, 5), a = 10, b = 5

\frac{x ^{2}}{9} + \frac{y ^{2}}{64} = 1

4 x^{2} + 3 y^{2} + 24 x + 36 y + 72 = 0

a^{2} + 2 b^{2} = 10

\frac{x ^{2}}{12} + \frac{y ^{2}}{8} = 1

225 x^{2} + 576 y^{2} = 176400

What is x^2+4y^2+20x-40y=-100 ?
The solution to x^2+4y^2+20x-40y=-100 is Ellipse with (h,k)=(-10,5),a=10,b=5